Some of the metal perchlorates are of low solubility, and should you want to prepare the picrate salt pure, and not in solution, looking at the solubility of each will be very important. Personally I would use the carbonates as you have no other ions in solution after loss of carbonate as CO2 and H2O. But since it appears you only need an aqueous solution of the picrate, starting with nitrate, carbonate, perchlorate, will all work.
I have posted impact sensitivities for picrate salts in another thread, and for the most part they are overrated. Exception: lead, silver, mercury, thallium, but we are still talking hammer hit to set off, not spontaneous explosions.